20. A found that 1o os choshey had met their partner thro Australian pet ownersf

Question

20. A found that 1o os choshey had met their partner thro Australian pet ownersfrande to Animals (RSP that lily d the 95% confid rough o h pet (RSPCA 2005). Find hgh owners who fintu ustral n reeption) tests for the ability of xts to fvidual. This test uses five cards with diohe the pet interval for the proportion of A love through their pets One classical experiment on ESp 21. to show telepathy -to read the mind ent designs, all known to both di trial, the "sender" sees a randomly coos and concentrates on its design. Thecard attempts to guess the identity of the careVer' of the five cards is equally likely to be chosen individual both participants. In a chosen card ach and only one card is the correct answer at point a. Out of 10 trials, a receiver got four cards correct. What is her success rate? What is her expected rate of success, assuming she i only guessing? html

Explanation / Answer

Question 21

here there are five cards and only one card is correct here.

(a) Here proportion of correct card received = 4/10 = 0.4

success rate = 40%

Expected rate of success, if he is just guessing = 1/5 = 20%

(b) Here the hypothesis are

Null Hypothesis : success rate is same as the success rate while guessing. p = 0.20

ALternative Hypothesis : Success rate is higher as we assume the person has telepathic abiltities p > 0.20

so here n is very small so we will assume binomial distribution

Pr(x >= 4 ; 10 ; 0.2) = 1 - Pr(x < 4 ; 10 ; 0.2) = 1 - 0.8791 = 0.1209

so here at the 0.05 significance level we cannot say that Success rate is higher than the guessing probability 0.2.

(c) Here

the sample proportion p = 350/1000 = 0.35

standard error of proportion = sqrt (0.2 * 0.8/1000) = 0.01265

Test statsitic

Z = (0.35 - 0.2)/0.01265 = 11.8585

so here

p - value = Pr(Z > 11.8585) = 0.0000

so here p - value is less than 0.05 so here it is very significance here.

As we can notice here that the success rate (35%) is less than the success rate of previous question (40%) biut here the sample size is very very large as compared to previous question. As per law of large numbers, the mean value will tend to go to the average value when we progresses. so this is not contradiction, it is just the correct method.

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